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Home office expense would be recorded by the partner of the partnership, not the partnership itself.
If the partnership rented office space then it would deduct it as rental expense. But if it was not rented, and a partner used his/her home for business use then that respective partner may be eligible to deduct the business use of home on his/her individual income tax return.
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Correct the partner would compute his/her business use of home deduction and enter it as "UPE" on Schedule E. see page E-9 of the the following instructions - http://www.irs.gov/pub/irs-pdf/i1040se.pdf